Cooling has a half-life: each equal time-slice closes the same fraction of the temperature gap.
Newton’s law of cooling is exponential. If a drink covers half the gap to fridge temperature in 15 minutes, it covers half the remainder in the next 15.
Newton's law of cooling holds for small temperature differences with convection doing the work. At a large difference radiation takes over and scales with the fourth power of absolute temperature, so a red-hot billet cools far faster at first than any exponential predicts.
At 80 °C the rule says 600 W/m² and the exact answer is 1,017 W/m² — 41% low. It is never within 10% anywhere in this range.
Equal fractions in equal times is Newton’s law, and Newton’s law only counts convection. Radiation goes as the FOURTH power of absolute temperature, so it is a rounding error on a warm mug and a third of the loss on something hot. The half-life is only constant while the thing is nearly cold.
The rule against the exact answer, computed across the range. Inside the shaded band the shortcut is close enough to use; outside it, reach for the calculator.
Estimate with the rule, then check it against the calculator that models it properly.
Open Beverage Cooling Simulator →